地貌及等高线表示的分解定理与表现定理

The Decomposition Theorem and Representation Theorem of Contours of Topographic Features

随着计算机制图和GIS的迅速发展 ,对于有着广泛应用的地貌形态特征问题 ,提出了进一步加以科学、系统、深入定量研究的迫切要求 ,以便获得更科学、合理的应用。作为一个系列研究的开始 ,首先要解决用 2维空间的等高线表示 3维空间地貌形态的科学性这一问题。为此 ,文中引入了地貌截影及截地貌的概念 ,通过地貌分解定理与表现定理的证明 ,以及等高线、地貌截影和截地貌三者之间的等价关系的论述 ,最终从数学上解决了上述基本问题 。

With the rapid development of computer assisted mapping and GIS, a scientific, systematic and definite quantitative study of topographic features which is widely used, is urgently needed so that it can be used more sicentifically.The basic problem, the feasibility of expressing three dimensional topographic features by the contours of two dimensional space should be solved as a start of a series of studies. In this paper, the concepts of the cross section of topographic features are introduced. And then through the proof of the decomposition theorem and representation theorem and the description of the equivalent relations among the contours and cross sections of topographic features as well as cut topographic features, the problem is solved at last.Thus a foundation has been laid for further studies.